Remember when Picard dated a subordinate, then decided he had to kick her out of a highly coveted post on the flagship of the Federation because he liked her too much?
Picard was shagging Lt. Cmdr Darren in Lessons, and she was his direct subordinate (unless you consider that she technically works for Riker). Then he transferred her when it got a little difficult.
Both prove my point. Even
Picard realized that it wasn't appropriate to date a subordinate as it impacted his ability to command, his decision making and even
impacted a woman's career in the end. Darren went from a prestigious position on the Federation flagship, virtually the pinnacle of her field and it all ended because the Captain sought to date a subordinate.
And while Starfleet seemingly has no direct rule against this it's just good "business practice" to not let it happen and Picard let it happen to him in a moment of weakness and look how it turned out?
Now, you could use this to argue Picard can't date
anybody on the ship and I'd agree since the entire ship is pretty much his direct subordinate, but I could argue that
maybe the senior staff aren't exactly subordinates but mostly "on the same level" as him (as is everyone else to one another.) So it wouldn't be inappropriate for Picard to date, say, Crusher as it wouldn't create too much conflict of interest when it came to ship operations and missions.
But Picard's interest in Darren could have impacted a mission and certainly impacted a career (I believe in the same episode it's even shown that a degree or two of "favoritism" to Darren impacted ship operations.)
If Geordi started dating a
direct subordinate that'd create a mess of problems for him, his other staff members and for his department. Say she made a mistake and something almost blew up, data was lost or something even trivial but otherwise annoying almost happened and it was caused by Ensign McCrushy there. How could Geordi lay down corrective action to someone he is involved with? How could he field complaints about her work from other members of his staff? How comfortable would his staff be to point out her mistakes and errors? It'd have a very real impact on ship operations, Geordi had good reason to not show any interest in her or to seek a relationship with her.
If she was in someone else's department that'd be a completely different, and more appropriate, situation.
